Question: Rip van Winkle has fallen asleep for a very long time.
The length of his beard (in millimeters) as a function of time (in weeks) is graphed.
Beard length (millimeters)
Time (weeks)
How long did it take each time Rip van Winkle's beard grew by 5 millimeters?
Choose 1 answer:
A 2.5 weeks
B 7.5 weeks
C 5 weeks
D 2 weeks
Graph: a line increasing from about $(0, 10)$ to about $(30, 85)$, shown in the top-center; position_hint = top-right.
1. **State the problem:** We want to find how long it takes for Rip van Winkle's beard to grow by 5 millimeters based on the graph showing beard length over time.
2. **Identify points from the graph:** The beard length increases from approximately $(0, 10)$ to $(30, 85)$.
3. **Calculate the total growth in beard length:**
$$85 - 10 = 75 \text{ millimeters}$$
4. **Calculate the total time elapsed:**
$$30 - 0 = 30 \text{ weeks}$$
5. **Find the rate of growth per week:**
$$\text{Rate} = \frac{\text{Change in length}}{\text{Change in time}} = \frac{75}{30} = 2.5 \text{ millimeters per week}$$
6. **Find the time it takes to grow 5 millimeters:**
$$\text{Time} = \frac{\text{Growth amount}}{\text{Rate}} = \frac{5}{2.5} = 2 \text{ weeks}$$
7. **Answer:** It takes 2 weeks for the beard to grow by 5 millimeters.
**Final answer: D 2 weeks**